About the Editors XV List of Contributors XVII Preface XXIII Part I: Fundamentals 1 1 Quantum Spin Hall Effect and Topological Insulators 3 Frank Ortmann, Stephan Roche, and Sergio O. Valenzuela References 9 2 Hybridization of Topological Surface States and Emergent States 11 Shuichi Murakami 2.1 Introduction 11 2.2 Topological Phases and Surface States 12 2.2.1 Topological Insulators and Z 2 Topological Numbers 12 2.2.2 Weyl Semimetals 13 2.

2.3 Phase Transition between Topological Insulators and Weyl semimetals 15 2.3 Hybridization of Topological Surface States and Emergent States 19 2.3.1 Chirality of the Surface Dirac Cones 19 2.3.2 Thin Film 20 2.3.

3 Interface between Two TIs 21 2.3.4 Superlattice 25 2.4 Summary 28 Acknowledgments 29 References 29 3 Topological Insulators in Two Dimensions 31 Steffen Wiedmann and Laurens W. Molenkamp 3.1 Introduction 31 3.2 2D TIs: Inverted HgTe/CdTe and Inverted InAs/GaSb Quantum Wells 33 3.2.

1 HgTe/CdTe QuantumWells 33 3.2.2 The System InAs/GaSb 35 3.3 Magneto-Transport Experiments in HgTe QuantumWells 36 3.3.1 Sample Fabrication 36 3.3.2 Transition from n - to p -Conductance 37 3.

3.3 Magnetic-Field-Induced Phase Transition 38 3.4 The QSHeffect in HgTe QuantumWells 40 3.4.1 Measurements of the Longitudinal Resistance 41 3.4.2 Transport in Helical Edge States 43 3.4.

3 Nonlocal Measurements 44 3.4.4 Spin Polarization of the QSH Edge States 45 3.5 QSH Effect in a Magnetic Field 45 3.6 Probing QSH Edge States at a Local Scale 48 3.7 QSH Effect in InAs/GaSb QuantumWells: Experiments 49 3.8 Conclusion and Outlook 51 Acknowledgements 52 References 52 4 Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators 55 M. Zahid Hasan, Su-Yang Xu, and Madhab Neupane 4.

1 Introduction 55 4.2 Z 2 Topological Insulators 58 4.3 Topological Kondo Insulator Candidates 69 4.4 Topological Quantum Phase Transitions 74 4.5 Topological Dirac Semimetals 76 4.6 Topological Crystalline Insulators 84 4.7 Magnetic and Superconducting Doped Topological Insulators 89 Acknowledgements 95 References 96 Part II: Materials and Structures 101 5 Ab Initio Calculations of Two-Dimensional Topological Insulators 103 Gustav Bihlmayer, Yu. M.

Koroteev, T. V.Menshchikova, Evgueni V. Chulkov, and Stefan Blügel 5.1 Introduction 103 5.2 Early Examples of 2D TIs 104 5.2.1 Graphene and the Quantum Spin Hall Effect 104 5.

2.2 HgTe: Band Inversion and Topology in a 2D TI 108 5.3 Thin Bi and Sb Films 112 5.3.1 Bilayers 112 5.3.2 Thicker Layers 115 5.3.

3 Alloyed Layers 118 5.3.4 Supported Layers 119 5.4 Compounds 121 5.4.1 Binary Compounds of A2B3 Type 122 5.4.2 Ternary Compounds: A'A2B4 and A' 2A2B4 Types 124 5.

5 Summary 125 Acknowledgments 126 References 126 6 Density Functional Theory Calculations of Topological Insulators 131 Hyungjun Lee, David Soriano, and Oleg V. Yazyev 6.1 Introduction 131 6.2 Methodology 132 6.2.1 Foundations of Density Functional Theory 132 6.2.2 Practical Aspects of DFT Calculations 136 6.

2.3 Including Spin-Orbit Interactions 139 6.2.4 Calculating Z 2 Topological Invariants 143 6.3 Bismuth Chalcogenide Topological Insulators: A Case Study 144 6.3.1 Bulk Band Structures of Bi2Se3 and Bi2Te3 144 6.3.

2 Topologically Protected States at the (111) Surface of Bismuth Chalcogenides 148 6.3.3 Nonstoichiometric and Functionalized Terminations of the Bi2Se3 (111) Surface 151 6.3.4 High-Index Surfaces of Bismuth Chalcogenides 155 6.4 Conclusions and Outlook 156 References 157 7 Many-Body Effects in the Electronic Structure of Topological Insulators 161 Irene Aguilera, Ilya A. Nechaev, Christoph Friedrich, Stefan Blügel, and Evgueni V. Chulkov 7.

1 Introduction 161 7.2 Theory 163 7.3 Computational Details 166 7.4 Calculations 167 7.4.1 Beyond the Perturbative One-Shot GW Approach 167 7.4.2 Analysis of the Band Inversion 169 7.

4.3 Treatment of Spin-Orbit Coupling 170 7.4.4 Bulk Projected Band Structures 174 7.4.4.1 Bi2Se3 175 7.4.

4.2 Bi2Te3 179 7.4.4.3 Sb2Te3 182 7.5 Summary 184 Acknowledgments 187 References 187 8 Surface Electronic Structure of Topological Insulators 191 Philip Hofmann 8.1 Introduction 191 8.2 Bulk Electronic Structure of Topological Insulators and Topological Crystalline Insulators 192 8.

3 Bulk and Surface State Topology in TIs and TCIs 194 8.4 Surface Electronic Structure in Selected Cases 198 8.4.1 Bi Chalcogenite-Based Topological Insulators 198 8.4.2 The Group V Semimetals and Their Alloys 200 8.4.3 Other Topological Insulators 203 8.

4.4 Topological Crystalline Insulators 203 8.5 Stability of the Topological Surface States 207 8.5.1 Stability with Respect to Scattering 207 8.5.2 Stability of the Surface States'' Existence 208 Acknowledgements 211 References 211 9 Probing Topological Insulator Surface States by Scanning Tunneling Microscope 217 Hwansoo Suh 9.1 Introduction 217 9.

2 Sample Preparation Methods 219 9.3 STM and STS on Topological Insulator 220 9.3.1 Topography and Defects 221 9.3.2 STS and Band Structure of Topological Insulators 223 9.3.3 Landau Quantization of Topological Surface States 225 9.

4 Conductance Map Analysis of Topological Insulator 229 9.4.1 Magnetically Doped Topological Insulator 233 9.4.2 Superconductor, Topological Insulator, and Majorana Zero Mode 235 9.5 Conclusions 236 References 237 10 Growth and Characterization of Topological Insulators 245 Johnpierre Paglione and Nicholas P. Butch 10.1 History of Bismuth-Based Material Synthesis 245 10.

2 Synthesis and Characterization of Crystals and Films 246 10.3 Native Defects and Achieving Bulk Insulation 252 10.4 New Material Candidates and Future Directions 256 References 260 Part III: Electronic Characterization and Transport Phenomena 265 11 Topological Insulator Nanostructures 267 Seung Sae Hong and Yi Cui 11.1 Introduction 267 11.2 Topological Insulators: Experimental Progress and Challenges 268 11.3 Opportunities Enabled by Topological Insulator Nanostructures 270 11.4 Synthesis of Topological Insulator Nanostructures 271 11.4.

1 Vapor-Phase Growth 271 11.4.2 Solution-Phase Growth 273 11.4.3 Exfoliation 273 11.4.4 Heterostructures 274 11.4.

5 Doping and Alloying 275 11.5 Fermi Level Modulation and Bulk Carrier Control 276 11.6 Electronic Transport in Topological Insulator Nanostructures 279 11.6.1 Weak Antilocalization and Magnetic Topological Insulators 280 11.6.2 Shubnikov-de Haas Oscillations 280 11.6.

3 Insulating Behavior at Ultrathin Limit 283 11.6.4 Aharonov-Bohm Effect and 1D Topological States 283 11.6.5 Superconducting Proximity Effect in TI Nanodevices 286 11.7 Applications and Future Perspective 286 11.8 Conclusion 288 References 289 12 Topological Insulator Thin Films and Heterostructures: Epitaxial Growth, Transport, and Magnetism 295 Anthony Richardella, Abhinav Kandala, and Nitin Samarth 12.1 Introduction 295 12.

2 MBE Growth of Topological Insulators 297 12.2.1 HgTe 299 12.2.2 Bi and Sb Chalcogenides 300 12.2.2.1 Bi2Se3 303 12.

2.2.2 Bi2Te3 303 12.2.2.3 Sb2Te3 304 12.2.2.

4 (Bi1− x Sb x )2Te3 305 12.2.2.5 Film Growth, Quality, and Stability 305 12.3 Transport Studies of TIThin Films 306 12.3.1 Shubnikov-de Haas Oscillations 308 12.3.

2 Quantum Corrections to Diffusive Transport in 3D TI Films 309 12.3.3 Mesoscopic Transport in 3D TI Films 310 12.3.4 Hybridization Gaps in Ultrathin 3D TI Films.